Details
| Original language | English |
|---|---|
| Pages (from-to) | 771-811 |
| Number of pages | 41 |
| Journal | Canadian journal of mathematics |
| Volume | 57 |
| Issue number | 4 |
| Publication status | Published - Aug 2005 |
Abstract
We study closed extensions A of an elliptic differential operator A on a manifold with conical singularities, acting as an unbounded operator on a weighted Lp-space. Under suitable conditions we show that the resolvent (λ - A)-1 exists in a sector of the complex plane and decays like 1/|λ| as |λ| → ∞. Moreover, we determine the structure of the resolvent with enough precision to guarantee existence and boundedness of imaginary powers of A. As an application we treat the Laplace-Beltrami operator for a metric with straight conical degeneracy and describe domains yielding maximal regularity for the Cauchy problem u̇ - Δu = f, u(0) = 0.
Keywords
- Manifolds with conical singularities, Maximal regularity, Resolvent
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Canadian journal of mathematics, Vol. 57, No. 4, 08.2005, p. 771-811.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - The resolvent of closed extensions of cone differential operators
AU - Schrohe, E.
AU - Seiler, J.
N1 - Copyright: Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2005/8
Y1 - 2005/8
N2 - We study closed extensions A of an elliptic differential operator A on a manifold with conical singularities, acting as an unbounded operator on a weighted Lp-space. Under suitable conditions we show that the resolvent (λ - A)-1 exists in a sector of the complex plane and decays like 1/|λ| as |λ| → ∞. Moreover, we determine the structure of the resolvent with enough precision to guarantee existence and boundedness of imaginary powers of A. As an application we treat the Laplace-Beltrami operator for a metric with straight conical degeneracy and describe domains yielding maximal regularity for the Cauchy problem u̇ - Δu = f, u(0) = 0.
AB - We study closed extensions A of an elliptic differential operator A on a manifold with conical singularities, acting as an unbounded operator on a weighted Lp-space. Under suitable conditions we show that the resolvent (λ - A)-1 exists in a sector of the complex plane and decays like 1/|λ| as |λ| → ∞. Moreover, we determine the structure of the resolvent with enough precision to guarantee existence and boundedness of imaginary powers of A. As an application we treat the Laplace-Beltrami operator for a metric with straight conical degeneracy and describe domains yielding maximal regularity for the Cauchy problem u̇ - Δu = f, u(0) = 0.
KW - Manifolds with conical singularities
KW - Maximal regularity
KW - Resolvent
UR - http://www.scopus.com/inward/record.url?scp=24144496907&partnerID=8YFLogxK
U2 - 10.4153/CJM-2005-031-1
DO - 10.4153/CJM-2005-031-1
M3 - Article
AN - SCOPUS:24144496907
VL - 57
SP - 771
EP - 811
JO - Canadian journal of mathematics
JF - Canadian journal of mathematics
SN - 0008-414X
IS - 4
ER -